Cost and Technical Efficiency of German Hospitals: Does Ownership Matter Annika herr* Ruhr Graduate school in Economics. Ruhr-Universitat Bochum Universitat erlangen-Nurnberg This is a preprint of an article published in Health Economics 17: 1057-1071 Copyright(c)2008 John Wiley Sons Ltd http://www3.interscience.wileycom/journal/5749/home September 1, 2008 Abstract 15r the first to investigate both the technical and cost efficiency of more than general hospitals. More specifically, it deals with the question how hospital efficiency varies with ownership, patient structure, and other exogenous factors, which are neither inputs nor outputs of the production process. The empirical results for the years from 001 to 2003 indicate that private and non-profit hospitals are on average less cost efficient and less technically efficient than publicly owned hospitals. The hospital rankings based on estimated efficiency scores turn out to be negatively correlated with average length of stay, which is highest in private hospitals. The results are derived by conducting a Stochastic Frontier Analysis(SFA) assuming both Cobb-Douglas and translog production technologies nd using a newly available and multifaceted administrative German dataset KEYWORDS: Hospital Efficiency, Ownership, Stochastic Frontier Analysi JL:C13,I11,L33 1 Introduction Tight public budgets and increasing per capita expenditures due to technological change, more chronic diseases, and an ageing population characterise the challenges faced by the german health care system today. In 2003, hospital expenditures made up 59.2 billion euro, which amounts to 2.7% of the German GDP. Since per capita expenditures for health care have grown by 50% between 1993 and 2003, debates about reforms and inefficiency of the german health care system had started in the late nineties and have resulted in several health care reforms Address: Universitat Erlangen-Nurnberg, Lehrstuhl fur Wirtschaftspolitik, Lange Gasse 20, D-90403 Nurnberg Germany. Email: annika. herr@wiso. uni-erlangen de
Cost and Technical Efficiency of German Hospitals: Does Ownership Matter? Annika Herr∗ Ruhr Graduate School in Economics, Ruhr-Universit¨at Bochum and Universit¨at Erlangen-N¨urnberg This is a preprint of an article published in Health Economics 17: 1057-1071. Copyright (c) 2008 John Wiley & Sons Ltd. http://www3.interscience.wiley.com/journal/5749/home September 1, 2008 Abstract This paper is the first to investigate both the technical and cost efficiency of more than 1,500 German general hospitals. More specifically, it deals with the question how hospital efficiency varies with ownership, patient structure, and other exogenous factors, which are neither inputs nor outputs of the production process. The empirical results for the years from 2001 to 2003 indicate that private and non-profit hospitals are on average less cost efficient and less technically efficient than publicly owned hospitals. The hospital rankings based on estimated efficiency scores turn out to be negatively correlated with average length of stay, which is highest in private hospitals. The results are derived by conducting a Stochastic Frontier Analysis (SFA) assuming both Cobb-Douglas and translog production technologies and using a newly available and multifaceted administrative German dataset. Keywords: Hospital Efficiency, Ownership, Stochastic Frontier Analysis. JEL: C13, I11, L33 1 Introduction Tight public budgets and increasing per capita expenditures due to technological change, more chronic diseases, and an ageing population characterise the challenges faced by the German health care system today. In 2003, hospital expenditures made up 59.2 billion euro, which amounts to 2.7% of the German GDP. Since per capita expenditures for health care have grown by 50% between 1993 and 2003, debates about reforms and inefficiency of the German health care system had started in the late nineties and have resulted in several health care reforms. ∗Address: Universit¨at Erlangen-N¨urnberg, Lehrstuhl f¨ur Wirtschaftspolitik, Lange Gasse 20, D-90403 N¨urnberg, Germany. Email: annika.herr@wiso.uni-erlangen.de 1
This paper is the first to investigate both the technical and cost efficiency of more than 1, 500 German general hospitals. It deals with two questions: (1) what is the average degree of hospital inefficiency and (2)how does this vary with ownership, patient structure, and other exogenous factors, which are neither inputs nor outputs to the production process. Identification and sepa- ration of controllable and uncontrollable sources of performance variation is essential to improve performance, also in view of public policies. The factors affecting cost and technical inefficiency will be identified by conducting a cross sectional Stochastic Frontier Analysis(SFA)which exploits the newly available and multifaceted German hospital statistics provided by the Statistical Offices of the Lander for the period from 2000 to 2003. The results of the cross sectional models will then be compared to a similarly distributed panel model. In order to compare a large number of heterogeneous hospitals, we weight the cases treated in each hospital according to their severity The weights are constructed by exploiting information about patients' diagnoses and lengths of stay. To check the robustness of the signs of the efficiency variables, we estimate their influence on both cost and technical inefficiency and compare the results over the three years under study. For the same reason, different specifications of both models with different samples are estimated. In a last step, hospital specific efficiency scores are estimated and used to compare hospital rankings across different distributional assumptions and models The German hospital industry is characterised by the simultaneous existence of ership types. Following the definition of the Statistical Offices of the Lander, three hospital types occurring in Germany are distinguished: public, non-profit, and private hospitals. Non-profit hospitals are also private, i.e. non-public, but, in contrast to private hospitals, they are run by non-profit organisations such as churches or miners'associations. Thus, in this paper the term private is used synonymously for ' private for-profit. Over the last ten years an increasing num- ber of public hospitals have been privatised in Germany. From 1992 to 2003, the share of all public hospitals has decreased from 45% to 36% whereas the share of all private hospitals has increased from 15% to 25%. The share of non-profit hospitals has remained relatively constant over the same period of time. Public funding has decreased steadily for all ownership types, which forces hospitals to invest independently. From 1972 to 2003, the ratio of hospitals'financing resources relative to all expenses of the statutory health insurance decreased from 27% to 7. 2%(Clade, 2004 Since non-profit hospitals are, by definition, not allowed to accumulate profits(except for reinvest ments), they have more difficulty than private hospitals to take up credit from the capital market On the other hand, non-profit institutions are exempt from corporation tax and pay a reduced value-added tax rate of 7% for all other goods($$3-5 UStG and $$51-68 AO). Public hospitals face similar financial difficulties where debts are still publicly compensated in most cases Inefficiency is defined as the hospitals deviation from the estimated or constructed cost or production frontier. Given exogenous input prices and demand driven outputs, the cost frontier maps minimal costs possible. Following Farrell(1957), the production frontier maps maximum feasible output given input use. This definition of inefficiency is from an input-oriented point of view since we assume output being more easily influenced by German hospitals than inputs which holds especially for the number of beds and prices. When measuring cost efficiency, it is assumed that all hospitals seek to minimise costs(Coelli et al., 2005; Kumbhakar and Lovell, 2000) imposed and it is not necessary to know input prices; input quantities are suficien Our need to be When estimating technical efficiency, no assumptions about cost minimising behaviour need to be The relative performance of public versus private producers has been examined from different theoretical perspectives(e. g. Agency and Property Rights, Public Choice, and Organisation The- ories). Following different approaches, they all conclude that private firms produce more efficiently than public firms in unregulated markets(Villalonga, 2000), partly due to the duality between profit maximising behaviour and efficiency. Regarding non-profit hospitals'behaviour, Philipson 1Krankenhausstatistik: Grund- Diagnose- und Kostendaten, 2000-2003, Antrag am Forschungsdatenzentrum der Statistischen Landesamter Nr. 254-2005
This paper is the first to investigate both the technical and cost efficiency of more than 1,500 German general hospitals. It deals with two questions: (1) what is the average degree of hospital inefficiency and (2) how does this vary with ownership, patient structure, and other exogenous factors, which are neither inputs nor outputs to the production process. Identification and separation of controllable and uncontrollable sources of performance variation is essential to improve performance, also in view of public policies. The factors affecting cost and technical inefficiency will be identified by conducting a cross sectional Stochastic Frontier Analysis (SFA) which exploits the newly available and multifaceted German hospital statistics provided by the Statistical Offices of the L¨ander for the period from 2000 to 2003.1 The results of the cross sectional models will then be compared to a similarly distributed panel model. In order to compare a large number of heterogeneous hospitals, we weight the cases treated in each hospital according to their severity. The weights are constructed by exploiting information about patients’ diagnoses and lengths of stay. To check the robustness of the signs of the efficiency variables, we estimate their influence on both cost and technical inefficiency and compare the results over the three years under study. For the same reason, different specifications of both models with different samples are estimated. In a last step, hospital specific efficiency scores are estimated and used to compare hospital rankings across different distributional assumptions and models. The German hospital industry is characterised by the simultaneous existence of various ownership types. Following the definition of the Statistical Offices of the L¨ander, three hospital types occurring in Germany are distinguished: public, non-profit, and private hospitals. Non-profit hospitals are also private, i.e. non-public, but, in contrast to private hospitals, they are run by non-profit organisations such as churches or miners’ associations. Thus, in this paper the term ‘private’ is used synonymously for ‘private for-profit’. Over the last ten years an increasing number of public hospitals have been privatised in Germany. From 1992 to 2003, the share of all public hospitals has decreased from 45% to 36% whereas the share of all private hospitals has increased from 15% to 25%. The share of non-profit hospitals has remained relatively constant over the same period of time. Public funding has decreased steadily for all ownership types, which forces hospitals to invest independently. From 1972 to 2003, the ratio of hospitals’ financing resources relative to all expenses of the statutory health insurance decreased from 27% to 7.2% (Clade, 2004). Since non-profit hospitals are, by definition, not allowed to accumulate profits (except for reinvestments), they have more difficulty than private hospitals to take up credit from the capital market. On the other hand, non-profit institutions are exempt from corporation tax and pay a reduced value-added tax rate of 7% for all other goods (§§3-5 UStG and §§51-68 AO). Public hospitals face similar financial difficulties where debts are still publicly compensated in most cases. Inefficiency is defined as the hospital’s deviation from the estimated or constructed cost or production frontier. Given exogenous input prices and demand driven outputs, the cost frontier maps minimal costs possible. Following Farrell (1957), the production frontier maps maximum feasible output given input use. This definition of inefficiency is from an input-oriented point of view since we assume output being more easily influenced by German hospitals than inputs which holds especially for the number of beds and prices. When measuring cost efficiency, it is assumed that all hospitals seek to minimise costs (Coelli et al., 2005; Kumbhakar and Lovell, 2000). When estimating technical efficiency, no assumptions about cost minimising behaviour need to be imposed and it is not necessary to know input prices; input quantities are sufficient. The relative performance of public versus private producers has been examined from different theoretical perspectives (e.g. Agency and Property Rights, Public Choice, and Organisation Theories). Following different approaches, they all conclude that private firms produce more efficiently than public firms in unregulated markets (Villalonga, 2000), partly due to the duality between profit maximising behaviour and efficiency. Regarding non-profit hospitals’ behaviour, Philipson 1Krankenhausstatistik: Grund- Diagnose- und Kostendaten, 2000-2003, Antrag am Forschungsdatenzentrum der Statistischen Landes¨amter Nr. 254-2005. 2
and Posner(2006)analyse antitrust issues theoretically and find that the same incentives to re- strain trade exist in the non-profit sector as in the private(for-profit)sector. In his overview about non-profit ownership and hospital behaviour, Sloan(2000) also concludes that there is no clear em- pirical evidence for a difference between these two ownership types. Duggan(2000) uses a change in financing US hospitals to reveal that the difference between the three types is driven by the soft budget constraint of public hospitals. Empirical studies of US hospital efficiency(Zuckerman et al., 1994; Rosko, 1999, 2001, 2004; Ozcan et al., 1992; Rosko and Chilingerian, 1999; Folland and Hofler, 2001)using different estimation strategies come to the conclusion that investor-owne hospitals or private(proprietary)hospitals are less cost efficient than their respective base groups (different combinations of public, non-profit or non-profit teaching hospitals). To our knowledge there are only two studies applying this approach to measure technical efficiency of hospitals(Web- steret al., 1998; Brown, 2003). Brown finds non-profit hospitals to be the most technically efficient In Switzerland, hospital cost efficiency does not differ by ownership type(Farsi and Filippini, 2006 2008) The efficiency of german hospitals has only been investigated with Data Envelopment Analysis DEA)so far, and results with respect to the ownership type are mixed. Helmig and Lapsley (2001)use data from 1991 to 1996 aggregated on the three ownership types(public, non-profit and private) and measure the highest inefficiency scores for the group of private hospitals. Staat(2006) applies dea to two different samples of comparable hospitals in western Germany using data from 1994. Differences between ownership types are not significant when comparing group means of the estimated efficiency scores. This lack of precision may be attributed to small subsamples. Werblow and Robra(2006)calculate high saving potentials in non-medical departments using aggregated non-medical costs from 2004 differentiated by the three ownership types and 16 federal states(48 observations). Calculated mean efficiency varies greatly over ownership types and federal states On average, however, the group of public hospitals is least efficient compared to the other two The remainder of the paper is organised as follows: The estimation strategy is explained in Subsection 2.1, the dataset is described in Subsection 2.2, and the problem of adjusting cases for severity of illness is discussed in Subsection 2.3. The results are presented in Section 3. Section 4 tains conclusions 2 Estimation Strategy and Data 2.1 Estimation Strategy In the case of technical efficiency, the log-linear technical stochastic frontier assuming a Cobb- Douglas production function is defined as A+∑Anm江n i.e. for each hospital i the output yi (the weighted number of cases)is maximised given inputs I CLi,., IKi and given an environment characterised by standard normally distributed random noise vi and systematic hospital specific inefficiency ui. The inefficiency term ui is assumed to b truncated at zero to assure that efficiency is smaller than 1 To measure cost efficiency for each hospital i, the K input prices w;=wli,., wki of inputs r: are calculated. The cost frontier to be estimated is defined as C +n1 +By ln lki 2Kumbhakar and Lovell(2000) provide a complete summary of both the theory and techniques used in Stochastic Frontier Production, Cost, and Profit Analysis. Another detailed review is provided by Greene(1997)
and Posner (2006) analyse antitrust issues theoretically and find that the same incentives to restrain trade exist in the non-profit sector as in the private (for-profit) sector. In his overview about non-profit ownership and hospital behaviour, Sloan (2000) also concludes that there is no clear empirical evidence for a difference between these two ownership types. Duggan (2000) uses a change in financing US hospitals to reveal that the difference between the three types is driven by the soft budget constraint of public hospitals. Empirical studies of US hospital efficiency (Zuckerman et al., 1994; Rosko, 1999, 2001, 2004; Ozcan et al., 1992; Rosko and Chilingerian, 1999; Folland and Hofler, 2001) using different estimation strategies come to the conclusion that investor-owned hospitals or private (proprietary) hospitals are less cost efficient than their respective base groups (different combinations of public, non-profit or non-profit teaching hospitals). To our knowledge, there are only two studies applying this approach to measure technical efficiency of hospitals (Webster et al., 1998; Brown, 2003). Brown finds non-profit hospitals to be the most technically efficient. In Switzerland, hospital cost efficiency does not differ by ownership type (Farsi and Filippini, 2006, 2008). The efficiency of German hospitals has only been investigated with Data Envelopment Analysis (DEA) so far, and results with respect to the ownership type are mixed. Helmig and Lapsley (2001) use data from 1991 to 1996 aggregated on the three ownership types (public, non-profit and private) and measure the highest inefficiency scores for the group of private hospitals. Staat (2006) applies DEA to two different samples of comparable hospitals in western Germany using data from 1994. Differences between ownership types are not significant when comparing group means of the estimated efficiency scores. This lack of precision may be attributed to small subsamples. Werblow and Robra (2006) calculate high saving potentials in non-medical departments using aggregated non-medical costs from 2004 differentiated by the three ownership types and 16 federal states (48 observations). Calculated mean efficiency varies greatly over ownership types and federal states. On average, however, the group of public hospitals is least efficient compared to the other two groups. The remainder of the paper is organised as follows: The estimation strategy is explained in Subsection 2.1, the dataset is described in Subsection 2.2, and the problem of adjusting cases for severity of illness is discussed in Subsection 2.3. The results are presented in Section 3. Section 4 contains conclusions. 2 Estimation Strategy and Data 2.1 Estimation Strategy In the case of technical efficiency, the log-linear technical stochastic frontier assuming a CobbDouglas production function is defined as2 ln yi = β0 + X n βn ln xni + vi − ui , (1) i.e. for each hospital i the output yi (the weighted number of cases) is maximised given inputs xi = [x1i , . . . , xKi] and given an environment characterised by standard normally distributed random noise vi and systematic hospital specific inefficiency ui . The inefficiency term ui is assumed to be truncated at zero to assure that efficiency is smaller than 1. To measure cost efficiency for each hospital i, the K input prices wi = [w1i , . . . , wKi] of inputs xi are calculated. The cost frontier to be estimated is defined as ln Ci wki = β0 + X n6=k βn ln wni wki + βy ln yi + vi + ui , (2) 2Kumbhakar and Lovell (2000) provide a complete summary of both the theory and techniques used in Stochastic Frontier Production, Cost, and Profit Analysis. Another detailed review is provided by Greene (1997). 3
erved total adj the vectors of the respective coefficients to be estimated. Since a cost frontier must be linearl homogeneous in input prices, total costs and the other input prices wni are normalised by dividing them with one fixed input price Wki. Estimation results do not depend on this choice. Additionally, the more flexible translog production function is estimated adding interaction terms between the inputs and outputs to the frontier. These interaction terms capture different degrees of substitutability between inputs and possible increasing or decreasing returns to scale. 3 The translog cost function in a panel data setting" where the symmetry restriction that Bk= BI posed is defined by +∑Ah如t A1+5∑∑ m In -In (nya)2+A12003+ The literature offers several different approaches to model the non-negative systematic ineffi ciency component ui. This study follows an approach first suggested by Deprins and Simar(1989) assuming that hospital-specific factors zi=[2li,. zLil directly impact inefficiency. Formally, uiN*(=5, 02), i.e. ui has a normal distribution truncated at zero with mode 2i 5 varying over the hospitals and constant variance o,. Note that zi does not influence the deterministic part of the cost or technical frontier. These models are called 'normal truncated normal models since one component of the composite error is normally distributed, while the second is truncated normally distributed. In order to estimate our model, we use the one-step procedure by Huang and Liu (1994)which has been generalised to panel data by Battese and Coelli(1993, 1995) 4o Due to the assumption that the variance is constant, the signs of the coefficients correspond the signs of their marginal effects on the unconditional expected inefficiency(Wang, 2002) To derive the log likelihood function, it is necessary to assume that ui and vi are distributed independently of each other and of the regressors. Maximum Likelihood estimation delivers con- sistent parameter estimates, that means it allows inference about the deterministic part of the frontier and the impacts of the exogenous variables on inefficiency. Furthermore, the estimates allow us to compute hospital-specific cost(technical)efficiency scores CE(TEi)as the expected value of the efficiency conditional on the random composite error, i. e. CEi=Eexp(-uilui+ui Ei= Elexpl-uilvi-uil. These estimated scores, however, are inconsistent using cross sec- tional data because the variation associated with the distribution of (uivi t ui) is independent of i(Kumbhakar and Lovell, 2000). The inconsistency of the efficiency estimators can only be overcome with a long panel dataset that allows asymptotics along the time dimension 2.2 The Dataset The data used in this study are extracted from the annual hospital and patient statistics, which are collected and administered by the Statistical Offices of the Lander for the years 2000 to 2003. All German hospitals are, by statute, obliged to deliver this information($17b KHG). Our unbalanced samples consist of 1556 to 1635 general hospitals each year. Approximately 11%of the observations are dropped due to data inconsistencies, namely hospitals with zero costs for doctors or nurses(734 obs. ) where costs per nurse were higher than costs per doctor(additional 105 obs. ) and where the numbers of doctors and nurses were missing(90 obs. ) Exhibiting very short lengths of stay, these observations are mainly small private hospitals with a very specific organisational structure(e.g 3For a detailed discussion about functional form in production function analysis compare Griffin et al.(1987) 4 The translog panel production functio be derived analogously and is not presented
where Ci are the observed total adjusted costs of hospital i, yi is the output, and βn and βy are the vectors of the respective coefficients to be estimated. Since a cost frontier must be linearly homogeneous in input prices, total costs and the other input prices wni are normalised by dividing them with one fixed input price wki. Estimation results do not depend on this choice. Additionally, the more flexible translog production function is estimated adding interaction terms between the inputs and outputs to the frontier. These interaction terms capture different degrees of substitutability between inputs and possible increasing or decreasing returns to scale.3 The translog cost function in a panel data setting4 where the symmetry restriction that βkl = βlk is imposed is defined by ln Cit wkit = β0 + X n6=k βn ln wnit wkit + βy ln yit + 1 2 X n6=k X m6=k βnm ln wnit wkit ln wmit wkit + X n6=k βyn ln wnit wkit ln yit + 1 2 βyy(ln yit) 2 + βt2003 + vit + uit. (3) The literature offers several different approaches to model the non-negative systematic ineffi- ciency component ui . This study follows an approach first suggested by Deprins and Simar (1989) assuming that hospital-specific factors zi = [z1i , ..., zLi] directly impact inefficiency. Formally, ui ∼ N +(z 0 i δ, σ2 u ), i.e. ui has a normal distribution truncated at zero with mode z 0 i δ varying over the hospitals and constant variance σ 2 u . Note that zi does not influence the deterministic part of the cost or technical frontier. These models are called ‘normal truncated normal’ models, since one component of the composite error is normally distributed, while the second is truncated normally distributed. In order to estimate our model, we use the one-step procedure by Huang and Liu (1994) which has been generalised to panel data by Battese and Coelli (1993, 1995). Due to the assumption that the variance is constant, the signs of the coefficients correspond to the signs of their marginal effects on the unconditional expected inefficiency (Wang, 2002). To derive the log likelihood function, it is necessary to assume that ui and vi are distributed independently of each other and of the regressors. Maximum Likelihood estimation delivers consistent parameter estimates, that means it allows inference about the deterministic part of the frontier and the impacts of the exogenous variables on inefficiency. Furthermore, the estimates allow us to compute hospital-specific cost (technical) efficiency scores CEi (T Ei) as the expected value of the efficiency conditional on the random composite error, i.e. CEi = E[exp(−ui)|vi + ui ] (T Ei = E[exp(−ui)|vi − ui ]). These estimated scores, however, are inconsistent using cross sectional data because the variation associated with the distribution of (ui |vi ± ui) is independent of i (Kumbhakar and Lovell, 2000). The inconsistency of the efficiency estimators can only be overcome with a long panel dataset that allows asymptotics along the time dimension. 2.2 The Dataset The data used in this study are extracted from the annual hospital and patient statistics, which are collected and administered by the Statistical Offices of the L¨ander for the years 2000 to 2003. All German hospitals are, by statute, obliged to deliver this information (§17b KHG). Our unbalanced samples consist of 1556 to 1635 general hospitals each year. Approximately 11% of the observations are dropped due to data inconsistencies, namely hospitals with zero costs for doctors or nurses (734 obs.), where costs per nurse were higher than costs per doctor (additional 105 obs.), and where the numbers of doctors and nurses were missing (90 obs.). Exhibiting very short lengths of stay, these observations are mainly small private hospitals with a very specific organisational structure (e.g. 3For a detailed discussion about functional form in production function analysis compare Griffin et al. (1987). 4The translog panel production function can be derived analogously and is not presented. 4
beds rented out to self-employed physicians; only privately paid treatments like plastic surgery) Finally, the dataset is trimmed by excluding the observations with the highest and lowest 1% in weighted cases, beds, and length of stay(300 obs. ) By trimming with respect to the length of stay, we exclude many private hospitals with an average length of stay of one day. These hospitals are not comparable to the other general hospitals. Table 1 reports descriptive statistics of the final sample by ownership type for 2003. Summary statistics of a) the frontier parameters b)the exogenous variables, and c) further characteristics are reported Table 1: The Hospital Statistics: Mean values and standard deviations of selected variables of the year 2003 Total profit Private nean s.d. mean costs cases in 1.000 9.668.64 weighted cases [in 1,000 9.2578711679.508.505.73 06.23 total-adjusted-_costs in m 3730 2.11 number of doctors 574957497828 39.99 44.40 number of nurses 160.68157.5920962 0 142.9999.41 108.38 number of other staff 182420215101m13 4.856294652518448549564072935 price._other -start [in 1,000E] 4.75713424859142356438361012 15.47130415.7910.7214.3110.8717.7820.89 0.01 0.11 0.44 ast dumn 0.170.380.170.3 0.35 0.26 0.44 male ratio 560.090.5 0.570.100.560.13 ratio 0110.21008 0.17 0.45 0.42 0.27 her figures of interest occupancy rates length 9243678572479.533691009542 mortality rate 0.025 0.020.0260.010.0270.030.0180.0 total_adj-costs per bed [in1000493831.42964430.15902128.1493.67547 total-adj costs per weighted 29791,164 mple size N a: number of full time equivalent employees, a2: Total number of employees minus doctors minus nurses, b: costs per full time equivalent employee, c: Costs for medical requirements (including drugs, transplants, implants ) per bed, d: Equals one if a hospital is not incorporated in the federal hospital planning and does not receive any public absidies, e: Equals one if located in eastern Germany, including Berlin, f: The ratio of patients of 75 years of age or older to all patients treated. g: Number of inpatient days divided by the number of beds x 365 a) For a better comparability of the hospitals, total costs are adjusted by subtracting costs for research and ambulatory care from total hospital costs. These adjusted costs(totaladjusted-costs) only capture 'hospital and nursing charges'("pflegesatzfahige Kosten")which are reimbursed by the health insurance companies. These costs, however, are not differentiated by the type of care provided(e. g. acute care vs. rehabilitation care). Input prices for the labour variables medical services(price. doc), nursing services(price.nurse)and other staff(price.other staff)are calculated by dividing the costs incurred per group by its number of full-time equivalent employees. The price for capital (price- bed)is determined as the quotient of costs for all medical requirements sRegarding the log-linear specification, we thus decided not to impute any small values to the observations which ussing or zero. 6 The length of each inpatient stay is at least one day even if the patient does not stay overnight
beds rented out to self-employed physicians; only privately paid treatments like plastic surgery).5 Finally, the dataset is trimmed by excluding the observations with the highest and lowest 1% in weighted cases, beds, and length of stay (300 obs.). By trimming with respect to the length of stay, we exclude many private hospitals with an average length of stay of one day.6 These hospitals are not comparable to the other general hospitals. Table 1 reports descriptive statistics of the final sample by ownership type for 2003. Summary statistics of a) the frontier parameters, b) the exogenous variables, and c) further characteristics are reported. Table 1: The Hospital Statistics: Mean values and standard deviations of selected variables of the year 2003 Total Public non-profit Private variable mean s.d. mean s.d. mean s.d mean s.d. output/costs cases [in 1,000] 9.37 8.05 11.84 9.66 8.64 5.95 5.23 6.29 weighted cases [in 1,000] 9.25 7.87 11.67 9.50 8.50 5.73 5.30 6.23 total adjusted costs [in mio e] 28.50 3.01 37.30 3.91 25.00 1.90 16.40 2.11 inputs number of beds 281.00 222.23 345.85 267.29 264.68 162.78 164.58 178.04 number of doctorsa 57.49 57.49 78.28 106.19 47.94 39.99 30.67 44.40 number of nursesa 160.68 157.59 209.62 203.57 142.99 99.41 87.21 108.38 number of other staffa2 189.95 246.48 263.99 347.17 155.15 114.32 100.17 126.53 price docb [in 1,000e] 88.98 14.29 90.66 11.41 88.34 12.46 86.42 22.73 price nurseb [in 1,000e] 44.85 6.29 46.52 5.18 44.85 49.56 40.72 9.35 price other staffb [in 1,000e] 41.75 7.13 42.48 5.91 42.35 6.42 38.36 10.12 price bedc [in 1,000e] 15.47 13.04 15.79 10.72 14.31 10.87 17.78 20.89 exogenous variables no subsidies dummyd 0.06 0.23 0.02 0.14 0.01 0.11 0.27 0.44 east dummye 0.17 0.38 0.17 0.37 0.14 0.35 0.26 0.44 female ratio 0.56 0.09 0.55 0.07 0.57 0.10 0.56 0.13 plus75 ratiof 0.21 0.11 0.21 0.08 0.23 0.13 0.17 0.12 surgery ratio 0.44 0.28 0.45 0.25 0.42 0.27 0.44 0.36 other figures of interest occupancy rateg 0.75 0.10 0.76 0.09 0.75 0.09 0.73 0.17 nurse per bed ratio 0.54 0.15 0.56 0.12 0.54 0.15 0.49 0.21 av. length of stay per hosp. 9.24 3.67 8.57 2.47 9.53 3.69 10.09 5.42 mortality rate 0.025 0.02 0.026 0.01 0.027 0.03 0.018 0.02 total adj costs per bed [in 1000e] 93.28 31.42 96.44 30.15 90.21 28.14 93.67 54.47 total adj costs per weighted cases 2,979 1,164 2,930 801 3,160 937 3,158 1,742 Sample size N 1594 641 693 260 Source: Final sample of the Hospital Statistics, Statistical Offices of the L¨ander, Germany. a: number of full time equivalent employees, a2: Total number of employees minus doctors minus nurses, b: costs per full time equivalent employee, c: Costs for medical requirements (including drugs, transplants, implants) per bed, d: Equals one if a hospital is not incorporated in the federal hospital planning and does not receive any public subsidies, e: Equals one if located in eastern Germany, including Berlin, f: The ratio of patients of 75 years of age or older to all patients treated, g: Number of inpatient days divided by the number of beds x 365. a) For a better comparability of the hospitals, total costs are adjusted by subtracting costs for research and ambulatory care from total hospital costs. These adjusted costs (total adjusted costs) only capture ’hospital and nursing charges’ (”pflegesatzf¨ahige Kosten”) which are reimbursed by the health insurance companies. These costs, however, are not differentiated by the type of care provided (e.g. acute care vs. rehabilitation care). Input prices for the labour variables medical services (price doc), nursing services (price nurse) and other staff (price other staff ) are calculated by dividing the costs incurred per group by its number of full-time equivalent employees. The price for capital (price bed) is determined as the quotient of costs for all medical requirements 5Regarding the log-linear specification, we thus decided not to impute any small values to the observations which were missing or zero. 6The length of each inpatient stay is at least one day even if the patient does not stay overnight. 5
pharmaceutical drugs, medical instruments, transplants, etc )and the number of installed beds (beds ) 7 The technical efficiency frontier is constructed by choosing the number of weighted cases weighted cases, cp. following subsection)as the output variable. Additional to the labour variables described above, the number of installed beds is used as a proxy for capital input b)The erogenous variables concur in both models and are included to control for observable heterogeneity, and to measure their direct effects on inefficiency. First, public hospitals are com- pared to private and non-profit hospitals. Since public subsidies, in particular investments in the hospital's infrastructure, only have an intermediate effect on inefficiency, we use the subsidy sta- tus of the previous year(no. subst-1). A closer look at the non-subsidised hospitals reveals that private hospitals, while forming the minority in the overall sample(15%), are strongly overrepre- sented in this subgroup(76-80%). As a consequence of this observation, we include interactions of subsidy status with ownership type(e.g.(no-subsx private)t-1) to allow for heterogeneous effects The regional dummy(east) differentiates between hospitals located in eastern Germany(including Berlin)and those located in western Germany. Analogously to Zuckerman et al.(1994), the ratio of female patients (female ratio), of patients of at least 75 years of age(plus 75 ratio) and of patients receiving surgeries(surgery ratio) are used to control for further case-mix differences c)The nurse per bed ratio (nurse/bed), which had been shown to decrease efficiency(Farsi and Filippini, 2006), is minimal for private(for-profit)hospitals. The unweighted average length of stay in the final sample turns out to be 3.52 days higher in private than in public institutions in 2000 and declines over time(cf. figure 1). This decline may be due to the expected change payment schemes towards the capitation fee system introduced in 2004 th of Since the health insurance type cannot be observed in the data, it is assumed that privately and statutory ("gesetzlich)insured patients(10% and 85% of the German population in 2003, respectively)are proportionally distributed across all hospital ownership types 2.3 Constructing Case-Mix Weights Demographic and geographic factors and specialisation of hospitals constitute structural differences regarding the severity of illness of the patients and related treatment costs. Most authors add a scalar measure of patient mix, which is based on cost information, such as the Medicare Case-Mix Index(MCI)for US hospitals(Ozcan and Luke, 1992; Rosko, 1999, 2001, 2004) or similar indices for Finland and UK(Linna and Hakkinen, 1997; Linna, 1998; Jacobs, 2001) to their model. The number of beds given in the hospital statistics is the annual average of installed beds for inpatient treatment as opposed to semi-inpatient and post-inpatient treatment) independent of the source of funding. This number does neither include those beds rented out to external physicians nor does it reflect the number of actually used SThe German dataset neither provides information on a patient's DRG nor on costs per patient
(pharmaceutical drugs, medical instruments, transplants, etc.) and the number of installed beds (beds).7 The technical efficiency frontier is constructed by choosing the number of weighted cases (weighted cases, cp. following subsection) as the output variable. Additional to the labour variables described above, the number of installed beds is used as a proxy for capital input. b) The exogenous variables concur in both models and are included to control for observable heterogeneity, and to measure their direct effects on inefficiency. First, public hospitals are compared to private and non-profit hospitals. Since public subsidies, in particular investments in the hospital’s infrastructure, only have an intermediate effect on inefficiency, we use the subsidy status of the previous year (no subst−1). A closer look at the non-subsidised hospitals reveals that private hospitals, while forming the minority in the overall sample (15%), are strongly overrepresented in this subgroup (76-80%). As a consequence of this observation, we include interactions of subsidy status with ownership type (e.g. (no subs×private)t−1) to allow for heterogeneous effects. The regional dummy (east) differentiates between hospitals located in eastern Germany (including Berlin) and those located in western Germany. Analogously to Zuckerman et al. (1994), the ratio of female patients (female ratio), of patients of at least 75 years of age (plus75 ratio) and of patients receiving surgeries (surgery ratio) are used to control for further case-mix differences. c) The nurse per bed ratio (nurse/bed), which had been shown to decrease efficiency (Farsi and Filippini, 2006), is minimal for private (for-profit) hospitals. The unweighted average length of stay in the final sample turns out to be 3.52 days higher in private than in public institutions in 2000 and declines over time (cf. figure 1). This decline may be due to the expected change in payment schemes towards the capitation fee system introduced in 2004. Figure 1: Unweighted average length of stay by ownership type and year Since the health insurance type cannot be observed in the data, it is assumed that privately and statutory (“gesetzlich”) insured patients (10% and 85% of the German population in 2003, respectively) are proportionally distributed across all hospital ownership types. 2.3 Constructing Case-Mix Weights Demographic and geographic factors and specialisation of hospitals constitute structural differences regarding the severity of illness of the patients and related treatment costs. Most authors add a scalar measure of patient mix, which is based on cost information, such as the Medicare Case-Mix Index (MCI) for US hospitals (Ozcan and Luke, 1992; Rosko, 1999, 2001, 2004) or similar indices for Finland and UK (Linna and H¨akkinen, 1997; Linna, 1998; Jacobs, 2001) to their model.8 7The number of beds given in the hospital statistics is the annual average of installed beds for inpatient treatment (as opposed to semi-inpatient and post-inpatient treatment) independent of the source of funding. This number does neither include those beds rented out to external physicians nor does it reflect the number of actually used beds. 8The German dataset neither provides information on a patient’s DRG nor on costs per patient. 6
However, Medicare patients do not cover all available treatments such that the Mci might be biased In this paper, severity of illness weights are constructed using the average length of stay(los) of each inpatient diagnosis in Germany. A mean los by year and main diagnosis m = l,...,M (ICD-10 Version 2.0, three digits) over all N= 2, 290 German hospitals is calculated: los N2s,(daysmi/casesmi ). The mean length of stay over all diagnoses and all hospitals is denoted by losG. The weight Tm Josm is bigger(smaller)than one if the treatment of diagnosis m takes more(less) time than the overall average los. These weights rely on the idea that length of stay is a good proxy for resource use. However, weights of rehabilitation care diagnoses may b upward biased compared to their costs, while weights for severe cases with high mortality rates may be biased downwards. Comparing the variable cases with the number of cases of each diagnosis multiplied by Tm( denoted by weighted cases), between -7, 065 and 6, 250 cases(-60% and 140 are added due t 3 Result 3.1 Cross Sectional Analysi Cross section estimation results for the three years 2001 to 2003 are reported in Table 2(cost efficiency) and Table 3(technical efficiency ). The hypothesis that there is no inefficiency(which means ou=0)can be rejected for each year under study. Over the three years, the signs of most coefficient estimates coincide in both models. Although standard errors and point estimates differ between the years and the models, both tables show similar and consistent results. The estimated effect of input prices on the cost frontier and of the inputs on the technical frontier are presented in the first part of Tables 2 and 3. The variation across time within each model is small and all but two coefficients are significantly different from zero at a one per cent level. They also show the expected positive effects on the respective dependent variables. The coefficient estimates of the exogenous factors in the second part of Tables 2 and 3, are read as effects on inefficiency. First and most importantly, they reveal that both private and non-profit hospitals are less efficient than public hospitals in Germany. This finding confirms the results of international hospital efficiency studies. Although in germany the health insurance coverage of treatments is highly regulated and hospitals cannot negotiate prices, we find differences in the hospitals efficiency. Studies analysing profits and debts of german hospitals show that public hospitals face a much higher risk of insolvency and closure(Augurzky et al., 2004). One explanation of this paradox is the regulatory regime. The former system of cost reimbursement including per diem payments offers profit maximising hospitals an incentive to boost revenues by increasing the lengths of stay. This conclusion is derived from the descriptive statistics in Table 1, from Figure 1 and from the rank correlation matrix in the Appendix (Table A-2). The pairwise correlation matrix reveals that efficiency rankings are negatively correlated with length of stay by at least 43% at the 1% significance level across all models. Thus, a further decrease of the average lengths of stay in private hospitals due to the introduction of capitation fees in 2004 may reduce the differences in efficiency across the ownership types in the long run. This question will be left to further research when more data points are available and the transformation process has proceeded. Finally, one may argue that public authorities mainly privatised unprofitable hospitals in order to rehabilitate their finances. However, the calculated efficiency scores of the 43 privatised hospitals are, on average, only slightly below those of all other hospitals. The result that private hospitals are less efficient than public hospitals does not imply that hospitals which have been privatised are less or more efficient than if they had not been privatised gThe time index t is suppressed for ease of illustration
However, Medicare patients do not cover all available treatments such that the MCI might be biased. In this paper, severity of illness weights are constructed using the average length of stay (los) of each inpatient diagnosis in Germany. A mean los by year9 and main diagnosis m = 1, . . . , M (ICD-10 Version 2.0, three digits) over all N = 2, 290 German hospitals is calculated: losm = 1 N PN i=1(daysmi/casesmi). The mean length of stay over all diagnoses and all hospitals is denoted by losG. The weight πm = losm losG is bigger (smaller) than one if the treatment of diagnosis m takes more (less) time than the overall average los. These weights rely on the idea that length of stay is a good proxy for resource use. However, weights of rehabilitation care diagnoses may be upward biased compared to their costs, while weights for severe cases with high mortality rates may be biased downwards. Comparing the variable cases with the number of cases of each diagnosis multiplied by πm (denoted by weighted cases), between −7, 065 and 6, 250 cases (−60% and 140%) are added due to weighting. 3 Results 3.1 Cross Sectional Analysis Cross section estimation results for the three years 2001 to 2003 are reported in Table 2 (cost efficiency) and Table 3 (technical efficiency). The hypothesis that there is no inefficiency (which means σu = 0) can be rejected for each year under study. Over the three years, the signs of most coefficient estimates coincide in both models. Although standard errors and point estimates differ between the years and the models, both tables show similar and consistent results. The estimated effect of input prices on the cost frontier and of the inputs on the technical frontier are presented in the first part of Tables 2 and 3. The variation across time within each model is small and all but two coefficients are significantly different from zero at a one per cent level. They also show the expected positive effects on the respective dependent variables. The coefficient estimates of the exogenous factors in the second part of Tables 2 and 3, are read as effects on inefficiency. First and most importantly, they reveal that both private and non-profit hospitals are less efficient than public hospitals in Germany. This finding confirms the results of international hospital efficiency studies. Although in Germany the health insurance coverage of treatments is highly regulated and hospitals cannot negotiate prices, we find differences in the hospitals’ efficiency. Studies analysing profits and debts of German hospitals show that public hospitals face a much higher risk of insolvency and closure (Augurzky et al., 2004). One explanation of this paradox is the regulatory regime. The former system of cost reimbursement including per diem payments offers profit maximising hospitals an incentive to boost revenues by increasing the lengths of stay. This conclusion is derived from the descriptive statistics in Table 1, from Figure 1 and from the rank correlation matrix in the Appendix (Table A-2). The pairwise correlation matrix reveals that efficiency rankings are negatively correlated with length of stay by at least 43% at the 1% significance level across all models. Thus, a further decrease of the average lengths of stay in private hospitals due to the introduction of capitation fees in 2004 may reduce the differences in efficiency across the ownership types in the long run. This question will be left to further research when more data points are available and the transformation process has proceeded. Finally, one may argue that public authorities mainly privatised unprofitable hospitals in order to rehabilitate their finances. However, the calculated efficiency scores of the 43 privatised hospitals are, on average, only slightly below those of all other hospitals. The result that private hospitals are less efficient than public hospitals does not imply that hospitals which have been privatised are less or more efficient than if they had not been privatised. 9The time index t is suppressed for ease of illustration. 7
Table 2: Cost efficiency of German hospitals, 2001-2003 frontier estimates In price_docs 0.081 0.127 0.082 (0.034) In price_ staff 0.321 0.299 340 (0.034) (0.033) 0.217 0.279 0.239 01 1.018 0.980 constant 2.832 2.470 2.640 ffects on inefficiency private 016 2.164 2.140 (0.955) (1.047) non-profit 1.087 ( no subs× private)t-1 (0.968) (1.127) (no subs xnon-profit)t-1 4.283 3.603 (0.913) (no-_ public)t-1 (1.214) (1.580) (1.708) east 0.664 1.327 3.830 surgery ratio 2.677 -3.307 2.026 (1.298) female ratio 4.503 4.502 5.318 (2285 constant 1.078 2.575 2.463 Log likelihood 1.549 Standard errors in parentheses. Price for nursing staff used for normalisation of prices and costs
Table 2: Cost efficiency of German hospitals, 2001-2003. ln adjusted costs 2001 2002 2003 frontier estimates ln price docs 0.081 0.127 0.082 (0.033) (0.033) (0.034) ln price other staff 0.321 0.299 0.340 (0.034) (0.034) (0.033) ln price bed 0.217 0.279 0.239 (0.016) (0.014) (0.014) ln weighted cases 1.018 0.980 0.997 (0.009) (0.008) (0.009) constant -2.832 -2.470 -2.640 (0.100) (0.094) (0.100) effects on inefficiency private 2.016 2.164 2.140 (0.730) (0.955) (1.047) non-profit 1.087 0.962 1.229 (0.454) (0.541) (0.666) (no subs×private)t−1 1.893 2.725 2.812 (0.586) (0.968) (1.127) (no subs×non-profit)t−1 2.656 4.283 3.603 (0.913) (1.591) (1.499) (no subs×public)t−1 3.472 3.641 3.476 (1.214) (1.580) (1.708) east 0.692 0.664 0.439 (0.327) (0.441) (0.404) plus75 ratio 1.327 3.830 3.364 (0.837) (1.533) (1.618) surgery ratio -2.677 -3.307 -2.026 (0.868) (1.298) (0.945) female ratio -4.503 -4.502 -5.318 (1.518) (1.740) (2.285) constant -1.078 -2.575 -2.463 (0.878) (1.555) (1.688) Log likelihood 234 236 259 Obs. 1,556 1,549 1,565 Standard errors in parentheses. Price for nursing staff used for normalisation of prices and costs. 8
Table 3: Technical efficiency of German hospitals, 2001-2003 2001 frontier estimates In docs 0.184 (0.016) 0.095 0.097 (0.023) (0.023) In other staff 0.113 0.046 0.089 (0.019) (0.019) 0.619 4.342 4.314 4.314 (0.053) (0.056) ffects on inefficiency private 2883 2.884 non-profit 2.137 1.821 (no sub 1.565 2.735 (1.034) (no subs xnon-profit)t 2.356 3.587 3.046 (1.408) (no-_ public)t-1 4.409 4.233 (1.942) east -0.580 1.313 3.974 surgery ratio 3.492 3.337 -2.375 (1.251) (1.391) (1.193) female ratio -1915 (1.210) constant 3.181 -4.67 4.712 (2.365) (2750) Log likelihood Obs 1,556 1,549 Standard errors in parentheses
Table 3: Technical efficiency of German hospitals, 2001-2003. ln weighted cases 2001 2002 2003 frontier estimates ln docs 0.158 0.184 0.154 (0.016) (0.017) (0.015) ln care 0.072 0.095 0.097 (0.023) (0.023) (0.023) ln other staff 0.113 0.046 0.089 (0.018) (0.019) (0.019) ln beds 0.589 0.619 0.598 (0.024) (0.025) (0.023) constant 4.342 4.314 4.314 (0.053) (0.056) (0.051) effects on inefficiency private 3.182 2.883 2.884 (1.216) (1.311) (1.518) non-profit 2.137 1.821 1.947 (0.869) (0.901) (1.075) (no subs×private)t−1 1.565 2.735 2.286 (0.531) (1.034) (1.025) (no subs×non-profit)t−1 2.356 3.587 3.046 (0.885) (1.408) (1.402) (no subs×public)t−1 4.409 4.339 4.233 (1.651) (1.942) (2.184) east -0.001 -0.580 -1.395 (0.290) (0.501) (0.831) plus75 ratio 1.313 3.974 3.346 (0.797) (1.605) (1.658) surgery ratio -3.492 -3.337 -2.375 (1.251) (1.391) (1.193) female ratio -2.119 -1.915 -1.466 (1.073) (1.185) (1.210) constant -3.181 -4.673 -4.712 (1.578) ( 2.365) (2.750) Log likelihood 508 482 519 Obs. 1,556 1,549 1,565 Standard errors in parentheses. 9
Turning to the other exogenous factors, hospitals which had not received subsidies in the previous year are significantly more inefficient than those having been partly or fully subsidised independent of ownership type. Annual public funding negotations and obligations to justify spending may yield hospitals to produce more efficiently. Tables 2 and 3 display that technical and cost inefficiency are not affected by location. Looking at the patient characteristics, the ratio of patients who are more than 75 years old to all patients affects efficiency negatively. Higher female ratios and surgery ratios incorporate significantly higher efficiency. However, the patients characteristics could capture unobserved case-mix effects which have not been addressed by the weighting. Allowing for more flexibility in the underlying production technology, we estimated both models assuming a translog production function. Because of the various interaction terms which are highl correlated with each other, the cost model does not deliver precise estimates for the years 2001 and 2002 and the algorithm does not converge in 2003. That is why we only present the results of the production model, which confirm the results of the Cobb-Douglas specification with respect to the signs and significance of the exogenous variables, in Table A-1 in the Appendix 3.2 Panel data estimation The availability of a two(cost model)o and three(production model) years panel dataset allows us to apply the extended one-step approach by Battese and Coelli(1995). It is assumed that all variables, the inefficiency, and the error term vary over time leading to a quasi-pooled panel with solely the variance of the composite error assumed to be constant. Table 4 shows the corresponding results for technical and cost efficiency estimation including time year dummies capturing tech- nological change and change in inefficiency over time. The frontier coefficients, which are mostl. significant, are not presented. Concerning the signs of the estimated coefficients, the cross sectional results can be reproduced with higher precision due to more observations. In a panel data setting, both models deliver precise estimates when a translog production function is assumed(columns 1 and 3). Quality of treatment may differ across hospitals. Different efficiency studies includ ing quality measures reveal that quality has little impact on estimated outcomes(Zuckerman and Hadley, 1994; Vitaliano and Toren, 1996). In columns 2 and 4, the death rate is included to show that results do not depend on this type of quality or case-mix adjustments(cp. Section 3. 4) In addition to the above discussed results, the positive and significant signs of the year dur efficients in the production frontier show that there is technological change shifting the outwards. Additionally, technical efficiency is significantly increasing over time. In the cost the lack of precision of the year dummy may be due to the short panel. Given the short time period of the panel dataset and very small within hospital variation, the higher accuracy of the panel estimates may be misleading. Within variation of weighted cases, beds, doctors, nurses, and other staff from 2000 to 2003 explains on average 2% of the variables'means and 8% of the overall variation. For the cost model, this variation is even lower, since we can only analyse two out of the four years in a panel data setting. To overcome the possible underestimation of the standard errors in the panel model, the data could be clustered by hospital. Since the cross sectional results suggest that the effects of interest are significant at least at a 10% level for each year separately, we refrain from this approach. Furthermore, the estimated mean efficiency scores can still not be estimated consistently using such a short panel since asymptotic properties of the maximum likelihood estimators cannot be exploited. Once a longer panel dataset is available, thetrue fixed effects or the 'true' random effects models proposed by Greene(2005) may be able to fit the normal-truncated normal models as opposed to the half-normal distributed case discussed in Section 3.4. Because of the drawbacks described above, the following discussion is based on the preferred cross sectional results oSince the definition of the costs changed between 2001 and 2002, we can only use two out of the for he cost efficiency panel model
Turning to the other exogenous factors, hospitals which had not received subsidies in the previous year are significantly more inefficient than those having been partly or fully subsidised, independent of ownership type. Annual public funding negotations and obligations to justify spending may yield hospitals to produce more efficiently. Tables 2 and 3 display that technical and cost inefficiency are not affected by location. Looking at the patient characteristics, the ratio of patients who are more than 75 years old to all patients affects efficiency negatively. Higher female ratios and surgery ratios incorporate significantly higher efficiency. However, the patients’ characteristics could capture unobserved case-mix effects which have not been addressed by the weighting. Allowing for more flexibility in the underlying production technology, we estimated both models assuming a translog production function. Because of the various interaction terms which are highly correlated with each other, the cost model does not deliver precise estimates for the years 2001 and 2002 and the algorithm does not converge in 2003. That is why we only present the results of the production model, which confirm the results of the Cobb-Douglas specification with respect to the signs and significance of the exogenous variables, in Table A-1 in the Appendix. 3.2 Panel Data Estimation The availability of a two (cost model)10 and three (production model) years panel dataset allows us to apply the extended one-step approach by Battese and Coelli (1995). It is assumed that all variables, the inefficiency, and the error term vary over time leading to a quasi-pooled panel with solely the variance of the composite error assumed to be constant. Table 4 shows the corresponding results for technical and cost efficiency estimation including time year dummies capturing technological change and change in inefficiency over time. The frontier coefficients, which are mostly significant, are not presented. Concerning the signs of the estimated coefficients, the cross sectional results can be reproduced with higher precision due to more observations. In a panel data setting, both models deliver precise estimates when a translog production function is assumed (columns 1 and 3). Quality of treatment may differ across hospitals. Different efficiency studies including quality measures reveal that quality has little impact on estimated outcomes (Zuckerman and Hadley, 1994; Vitaliano and Toren, 1996). In columns 2 and 4, the death rate is included to show that results do not depend on this type of quality or case-mix adjustments (cp. Section 3.4). In addition to the above discussed results, the positive and significant signs of the year dummies’ coefficients in the production frontier show that there is technological change shifting the frontier outwards. Additionally, technical efficiency is significantly increasing over time. In the cost model, the lack of precision of the year dummy may be due to the short panel. Given the short time period of the panel dataset and very small within hospital variation, the higher accuracy of the panel estimates may be misleading. Within variation of weighted cases, beds, doctors, nurses, and other staff from 2000 to 2003 explains on average 2% of the variables’ means and 8% of the overall variation. For the cost model, this variation is even lower, since we can only analyse two out of the four years in a panel data setting. To overcome the possible underestimation of the standard errors in the panel model, the data could be clustered by hospital. Since the cross sectional results suggest that the effects of interest are significant at least at a 10% level for each year separately, we refrain from this approach. Furthermore, the estimated mean efficiency scores can still not be estimated consistently using such a short panel since asymptotic properties of the maximum likelihood estimators cannot be exploited. Once a longer panel dataset is available, the ‘true’ fixed effects or the ‘true’ random effects models proposed by Greene (2005) may be able to fit the normal-truncated normal models as opposed to the half-normal distributed case discussed in Section 3.4. Because of the drawbacks described above, the following discussion is based on the preferred cross sectional results. 10Since the definition of the costs changed between 2001 and 2002, we can only use two out of the four years in the cost efficiency panel model. 10
